Wednesday, September 26, 2012

1209.5564 (Amru Hussein et al.)

Quantum graphs with mixed dynamics: the transport/diffusion case    [PDF]

Amru Hussein, Delio Mugnolo
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly nonlocal couplings at the boundary. We provide sufficient conditions for these to be governed by a contraction semigroup on a Hilbert space naturally associated with the system. Subsequently, we devote our interest to further natural questions in the fields of parabolic and elliptic differential equations and eventually obtain a characterization of the sub-Markovian property and a description of the spectrum. We conclude the article showing that our setting is also adequate to discuss specific systems of diffusion equations with boundary delays.
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